Cross-Domain Stability Isomorphism in the Paton System

This paper formalises the structural isomorphism underlying Tier-7 domain instantiations within the Paton System. Across mathematics, physics, engineering, psychology, and organisational systems, regime stability is governed by identical admissibility conditions. A theorem-level formulation demonstrates that continuation within a regime occurs if and only if distributed load remains within tolerance capacity and invariants are preserved. Collapse or regime transition follows load concentration or invariant violation. The contribution is structural integration rather than empirical replacement, clarifying cross-domain stability as constraint-governed continuation under distributed load.